MIMO Synchronization Using Matrix Inverse Correlation
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Solution Overview
Problem
MIMO synchronization methods are complex and sub-optimal, especially in the presence of interference, due to the need for determinant calculation and matrix inversion, which becomes expensive as the number of antennas increases, and are not robust for non-orthogonal sequences.
Innovation Solution
A method for time/frequency synchronization in MIMO systems that calculates a correlation matrix, its inverse, and estimates noise and cross-correlation matrices to determine a synchronization criterion, reducing complexity by avoiding determinant calculations and optimizing performance through alternative receivers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If GLRT method is used for MIMO synchronization, then synchronization performance is improved, but device complexity increases due to determinant calculation and matrix inversion
Solution Approach 1:
The patent segments the complex GLRT synchronization problem into multiple simpler steps: first calculating correlation matrices Rss and Rxx, then computing their inverses, and finally using these inverses to calculate the synchronization criterion. This segmentation avoids direct determinant calculation while maintaining GLRT performance through the equivalent formulation involving matrix inverses.
Solution Approach 2:
The patent substitutes the mechanical computation of determinants (which is computationally expensive) with an equivalent mathematical approach using matrix inverses. The synchronization criterion is reformulated from a determinant-based expression to one involving Rss^-1 and Rxx^-1, replacing the mechanical determinant calculation with algebraic operations that are more efficient to compute.
2Productivity
If number of antennas increases, then MIMO system performance is improved, but computational cost increases due to matrix inversion
Solution Approach 1:
The patent performs preliminary calculations of the correlation matrices Rss and Rxx and their inverses before the actual synchronization decision. By pre-computing these matrices and storing their inverses, the system avoids repeated expensive matrix inversions during the synchronization process, thereby reducing computational cost while supporting increased numbers of antennas for improved MIMO performance.
3Device complexity
If MMSE method is used to reduce complexity, then device complexity is reduced, but measurement precision deteriorates for non-orthogonal sequences
Solution Approach 1:
The patent changes the mathematical parameters and formulation of the synchronization criterion to work effectively with non-orthogonal sequences. By using the generalized correlation matrix approach with Rss^-1 and Rxx^-1, the method adapts to non-orthogonal training sequences while maintaining synchronization accuracy, unlike simpler methods that assume orthogonality.
Data Source
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AI summary
The invention relates to a method allowing synchronisation in a transmission system comprising M transmitters and N receivers, in the presence of interferences, characterised in that it determines the value of the synchronisation criterion, taking into account the trace of a matrix resulting from the product formed by the inverse matrix of correlation of the learning sequences, the conjugated transpose of the estimate of the matrix of intercorrelation of the signals received and the learning sequences, and the inverse of an estimate of the noise matrix and the estimate of the matrix of intercorrelation between the observations and the learning sequences, with the criterion C(I, Δf) = EGLRT3(/,Δf) = formula (I).